Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
346 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. #17989510 | C4 | semidirect |
| 14. #17989509 | C4 | semidirect |
| 19. #17988408 | C4 | semidirect |
| 20. #17988407 | C4 | semidirect |
| 21. #364×C73 | C4 | semidirect |
| 123. C73 | #12659 | semidirect |
| 137. #364 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626270 | 2 |
| #22626146 | 2 |
| C4×#14556645 | 2 |
| #22624977 | 2 |
| #364×D73 | 2 |
| #12659 | 73 |